Talk:Diatonic scale

Archiving, and Diatonic and chromatic now established

I have now added a lot of older, and also more recent material, to an archive (see above). A new article has been set up, partly to deal with issues of terminology that have arisen here . Discussion about application of the terms diatonic and chromatic, as applied to intervals or to anything else, is best conducted in the context of that article. I suggest that we now discontinue any such general debate here (and at Talk:Interval (music), Talk:Diminished seventh, etc.), and confine it to Talk:Diatonic and chromatic. – Noetica^♬Talk 02:30, 29 March 2007 (UTC)

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Si?

It's Ti, wtf? Ti, a drink with jam and bread. —Preceding unsigned comment added by 75.72.21.221 (talk) 00:45, 14 November 2007 (UTC)

In the North American English I learned at my mother's knee, and other joints, the solfege of a Major scale is "Do Re Mi Fa Sol La Ti Do." I assume "Si" is used in other idioms. I believe the 5th scale degree is "Sol" everywhere, not "So" ... attention needed here from someone who actually knows. __Just plain Bill 17:41, 14 November 2007 (UTC)

It's Sol. The names were created by Guido D'Arezzo when he wrote his gamut based on a hymn to St. John. Si was changed to Ti to avoid confusion with Sol. Check Wikipedia article Solfège. Here's the hymn: Ut queant laxis resonare fibris, Mira gestorum famuli tuorum, Solve polluti labi reatum, Sancte Iohannes. Ut was also changed to Do. The word "solfa" designates the set of syllables (do, re, mi, etc.) that are sung to the respectives tones of the scale. Solfaing is singing the sol–fa syllables as a tune. See Do-Re-Mi.[User:Lestrade|Lestrade]] (talk) 19:23, 15 August 2008 (UTC)Lestrade

Steps and half-steps

Could someone please add a simple explanation to the article of what steps and half-steps are? Apparently I'm missing something because I never knew stairs had anything to do with music! :) DBlomgren 02:38, 31 May 2007 (UTC)

That's like asking a physicist for a simple explanation of gravity. Okay, it makes things fall down. A half step is the interval between two adjacent keys on the piano; a whole step is two half steps. In neither case (gravity or half steps) would we put it in the article because it's not technically accurate, but if it helps, here you go. —Wahoofive (talk) 03:58, 31 May 2007 (UTC)

Could be the old "nations separated by a common tongue" thing. I believe the Queen's English uses "whole tone" and "semitone" where we say whole steps and half steps. __Just plain Bill (talk) 20:36, 15 August 2008 (UTC)

I don't think so; we say semitone in the US, too. This 1897 book Music discusses the terms on p.401 (It's a Chicago magazine, complaining about a Pennsylvania teacher using "tone" instead of "step", evidence of preferences for each in the US at the time). Dicklyon (talk) 04:02, 16 August 2008 (UTC)

The United States has not adopted an official language. Perhaps Just plain Bill was referring to the overall trend and not saying that no one in the US had never said the word "semitone". Hyacinth (talk) 07:20, 16 August 2008 (UTC)

Merriam-Webster lists "semitone" [1] as dating from the 15th century and unhelpfully defines it as, "half step," while pointing to, "also: half step", but, surely incorrectly, dates "half step" [2] only to 1904 while more helpfully defining it as, "1/12 of an octave". Hyacinth (talk) 07:51, 16 August 2008 (UTC)

Lastly, the book you link to discusses preferred rather than actual usage. Hyacinth (talk) 23:45, 16 August 2008 (UTC)

Thanks, Dicklyon, for the interesting and persuasive link. It appears to be an American reviewing a book by a British author (Orlando A. Mansfield) but criticizing the American author (Prof. Hugh A. Clarke, Univ. of Penn.) of the introduction "for an inexcusable carelessness of terminology." BTW, Google books gives the text version of the preceding phrase in the same sentence as "… f urination in a small space …". --Jtir (talk) 20:42, 16 August 2008 (UTC)

Here is a fun one. Seems to be one American berating another, in 1853, because he "calls a tone a step, and a semitone a half step ; now, who ever heard of a step in music, or in sound?" Dicklyon (talk) 03:40, 18 August 2008 (UTC)

If you know what a whole tone and a semitone are pretending confusion at half step and whole step is most likely unnecessary, as something about the names seems to indicate their relative meaning... Hyacinth (talk) 07:15, 16 August 2008 (UTC)

Both terminologies are widely understood. Perhaps on first occurrence, the other could be given in parentheses. Simple. Tony (talk) 07:39, 16 August 2008 (UTC)

The violin teacher I live with says "half step" and "whole step" in the English she learned in 1950's Dorchester, Mass. I've never heard her say "semitone." Not saying no US speaker ever does, but the my inner linguistic anthropologist (il mio antropologo linguistico interno) notices a preponderance of "steps" in US vernacular. My inner linguistic missionary is also alive and well, but has little to say on this subject. "Both teminologies widely understood" pretty well sums it up. __Just plain Bill (talk) 15:23, 16 August 2008 (UTC)

Thanks, Hyacinth, for the links to m-w.com. Here is another: half tone (1621) -> "half step". (also)

So the phrase "half-tone step" that had been in the article is redundant.

And, Bill, both Idiot's and Dummies prefer "half step" and "whole step". Whole tone doesn't appear to be used by anyone except WP as a separate entry in common dictionaries, although dictionary.com does give a def from The American Heritage® New Dictionary of Cultural Literacy, Third Edition (edited by E. D. Hirsch, Jr.), and Idiot's says tone is another word for whole step. --Jtir (talk) 20:07, 18 August 2008 (UTC)

M-W reveals itself to be an unreliable source on this topic. Concluding that "whole tone" isn't used anywhere but Wikipedia seem hasty given your sample of three dictionaries. Hyacinth (talk) 23:37, 16 August 2008 (UTC)

One may presume Benward & Saker (2003), for example, don't use "whole tone", but for their use of "whole-tone scale". Hyacinth (talk) 22:12, 17 August 2008 (UTC)

OK, tone and semitone, whole step and half step. Do I notice an absence of UK speakers contributing to this tempestuous discussion? I'd go see about getting a cite for it in the major second article, but haven't the energy just now. __Just plain Bill (talk) 04:03, 18 August 2008 (UTC)

Done. Complaints, comments, corrections at Talk:Major second. --Jtir (talk) 20:01, 18 August 2008 (UTC)

Please elaborate on the key question of why Ionian and Aeolian (C & A scales) were selected

Four others (ie all but Locrian) also have either major or minor opening triads. The circle of fifths arguments needs explicating; there's something extremely interesting and necessary about tonality that can't be dismissed with cultural relativity and needs illuminating technically as far as pos...

Sean McHugh 02 (talk) 11:38, 19 October 2008 (UTC)

Maximally separated half steps

It is important to make clear, in the introduction, the concept of "maximally separated" half steps, so that no layman could think (not even for a moment) that this means "separated by 5 whole steps".

This is what I tried to do in my last edit. Notice that the definition given in the first sentence of the previous version of the intro was strongly misleading. The concept was better (but not clearly enough, IMO) explained only in the next sentences.

I am not saying that my edit is perfect, but at least now everyone should be able to understand, and the first sentence is a perfect definition with no ambiguity. The concept of "maximum separation" of the half steps is tricky. Either we explain it clearly, or we just avoid it altogether. If you wish to further simplify the intro, you can safely delete the sentence referring to it, because in my edit this concept is not anymore presented as the definition of the diatonic scale, but as a consequence of it, in a separate sentence. Paolo.dL (talk) 20:41, 24 June 2010 (UTC)

Additional citations

Why, what, where, and how does this article need additional citations for verification? Hyacinth (talk) 13:48, 10 March 2011 (UTC)

Tag removed. Hyacinth (talk) 08:54, 10 December 2011 (UTC)

Why? Because Wikipedia articles need all assertions to be verifiable. The article currently has only two verifiable references and one incomplete one.

What? It needs full inline citations from published works on the subject (i.e. reputable sources).

Where? At the end of most of the sentences.

How? In the form of footnotes. See the WP:MOS for guidance and a selection of other articles for examples. Without additional citations the article will not be considered for a quality rating higher than C class.

Tag reinstated. 83.104.249.240 (talk) 02:16, 3 November 2012 (UTC)

Actually, you're right Hyacinth. Refimprove was the wrong tag. I've replaced it with More footnotes. 83.104.249.240 (talk) 02:28, 3 November 2012 (UTC)

When a tag is added to an article a reason must be given in within the tag or on the talk page (or both) or the tag is redundant (no one needs a tag to tell them that an article with two citations has very few citations). Many editors are surprised when a justification for a tag is requested, but most tags mention in their documentation that reasons and details need be provided, and editors should not use tags without consulting the documentation. Hyacinth (talk) 04:35, 30 September 2019 (UTC)

Three? major scales and three? minor scales?

The article mentions "the three major scales (Ionian, Lydian, and Mixolydian)" and "the three minor scales (Dorian, Phrygian, and Aeolian)" and Locrian scales. I don't see in the article or another article any explanation of this classification of the diatonic scales. I don't see that 'major' and 'minor' are applied to Lydian, Mixolydian, Dorian, or Phrygian elsewhere. If there is such a classification and it is mentioned here, it needs to be explained. Thank you.CountMacula (talk) 11:25, 6 October 2012 (UTC)

@CountMacula: The Dorian (II), Phrygian (III), and Aeolian (VI) modes have a minor triad on the tonic in common, and the Ionian (I), Lydian (IV), and Mixolydian (V) have a major triad on the tonic in common. The Locrian mode (VII) is omitted because instead of a major or minor triad on the tonic it has a diminished triad. Hyacinth (talk) 04:58, 30 September 2019 (UTC)

@Hyacinth: Thank you, and I see that the article now reflects that.CountMacula (talk) 00:25, 1 October 2019 (UTC)

Score notation

Here is the scale on this page using the score tag. Perhaps more accessible than midi/png files.

ColinKinloch (talk) 14:30, 12 November 2013 (UTC)

hi oppp — Preceding unsigned comment added by 2002:182D:195D:1234:DC2F:8DF9:7E36:923F (talk) 02:13, 26 April 2014 (UTC)

Modes Table

Why the last column heading reads "Example"? In the context of this article, for each Mode, there is only one possibility of pitch class "sequencing".--Connection (talk) 20:08, 5 January 2015 (UTC)

These modes could be created on other notes by the use of accidentals. —Wahoofive (talk) 23:30, 5 January 2015 (UTC)

Most appreciated. What I want to clarify is that using accidentals will be a different "Tonic relative to major scale"? Considering first row, Major scale on C is unique, on D is unique, and so forth... Eventually on C# is also unique. Thank you in advance.--Connection (talk) 21:22, 8 January 2015 (UTC)

Revisions of the article

I summarize here my revisions of today and my justifications. I am perfectly aware that my changes require references. I am not very good at doing this, because I don't usually read elementary textbooks on music theory, and I hope that others will add references – I am quite sure that they can be found. In addition, my revisions remain open to improvements.

• Added (whole tone) and (semitone) after whole step and half step.
• Removed the mention of the Pythagorean tuning in the lede: (a) Pythagorean tuning is a property neither of the diatonic scale, nor of the cycle of fifths (which could also be formed of tempered fifths); (b) until recently, musical instruments always were tuned by ear, in any tuning or temperament; (c) the diffusion of the diatonic scale certainly is not a consequence of its being in Pythagorean tuning.
• Changed "piano keyboard" in "musical keyboard" and "white keys" in "lower (white) keys": they are not always white.
• "Western music" instead of "Western harmony"; from the "Middle Ages" instead of "Renaissance".
• Removed "diatonic functionality": this kind of functionality is not a property of the diatonic scale, but rather of tonality. See also Talk:Function_(music).
• Moved the second paragraph of the section "History" to a subsection "Middle Ages".
• Provided an explanation of the relation between the four medieval modes and the seven scales.
• Added a subsection "Renaissance", with details of the reform by Glarean. I am aware that Glarean's twelve scales can be explained otherwise, but the explanation given here certainly is one of the correct explanations. I have no other reference than Glarean's treatise itself, but I understand that WP does not like first-hand sources.
• Added a subsection "Modern" (which might not be the best term – it'll have to do for now). Details on the origin of common practice tonality really don't belong here: I kept this subsection minimal.
• Simplified the "Theory" section on two essential points:

– Connecting the description of transpositions to Glarean's theory.

– Removing the somewhat puzzling idea that the keyboard arrangement could simplify the system of key signatures, and the even more puzzling statement that it "allows the adjacent positioning of most of the diatonic whole-steps" (?).

• Suppressed the "Analysis" section and moved its (modified) content to "Theory": this had nothing to do with analysis.
• I changed the "mode" subsection in accordance with my conviction that it is improper to call "mode" what is merely a scale.
• What is described as "properties" of diatonic scales often derive from the fact that our theory is conceived for them; I tried to show that without changing too much...
• I drastically reduced the mentions of theories by David Rothenberg, Balzano and Erv Wilson, and Diatonic set theory, which do not really concern diatonic scales properly speaking. Links to the specific articles are all that is needed. For the same reason I removed the infobox in the lede, which concerned properties that do not belong to diatonic scales properly speaking.

In addition to the above,

• The mention of "syntonic commas" in the caption of the second figure (and the corresponding "+" in the notation) remains unclear. The syntonic commas describe the difference between Pythagoran tuning and just intonation, but the caption does not suggest this comparison. Both examples could be moved to the section on tuning – where I added a comment on the notes differing by a syntonic comma.
• I am not sure that the denominations of the degrees in the major scale (tonic, supertonic, mediant, etc.) belongs here: it does not describe properties of the diatonic scales, but of tonality itself.
• The reference to "tetrachords" should be emended. The notion, in Diatonic_and_chromatic#Diatonic_scales, that medieval theorists described diatonic scales in terms of Greek tetrachords is merely wrong. Correcting that will have to remain for later.

— Hucbald.SaintAmand (talk) 11:13, 18 February 2017 (UTC)

Tuning of the diatonic scale

User:Anthony_Appleyard must certainly be thanked for his attempts at improving the section on Tuning. It seems to me, however, that this section has major problems and should probably be rewritten entirely. The problem actually begins in the preceeding section, with a paragraph that used (years ago) to belong to the "Tuning" section:

"David Rothenberg conceived of a property of scales he called propriety, and around the same time Gerald Balzano independently came up with the same definition in the more limited context of equal temperaments, calling it coherence. These properties may be considered to generalize properties of the diatonic scale to other scales. The generation of the diatonic scale by iterations of a single generator, the fifth, has also been generalized by Erv Wilson, in what is sometimes called a MOS scale. See also Diatonic set theory for a discussion of other properties that transcend the diatonic scale properly speaking."

Unless one would explain what these "properties" called "propriety" or "coherence" are, I find the first phrases of this paragraph perplexing – especially in view of the mention of "equal temperament", a temperament conceived for the chromatic scale. The links provided don't make the matter more understandable. As to the generation by fifths, it is not a specific property of the diatonic scale (not all diatonic scale are generated by fifths, while many non diatonic scales are), and "MOS scales" have little to do here. I don't see why it is necessary to mention here properties that "transcend" (???) the diatonic scale properly speaking. It seems to me that the paragraph could be replaced by a few "See also" links.

It the Tuning section itself, I am once again perplexed by the following statement:

"In many diatonic scales, after starting at a note, jumping upwards by a perfect fifth 12 times ends up a little higher than 7 octaves above the starting point. In the Pythagorean tuning and in Ptolemy's intense diatonic scale, the "little higher" is an interval called the Pythagorean comma (about 1.01364, about 0.2 of a semitone)."

First of all, since the lede (rightly) states that the diatonic scale can be obtained "using a chain of six perfect fifths", I don't see how one may jump twelve fifths in any diatonic scale. Jumping 12 fifths produces a chromatic scale. If the fifths are "perfect" (corresponding to 3:2), the resulting scale is in Pythagorean tuning and its end point indeed is a Pythagorean comma (and 7 octaves) higher than its starting point. On the other hand, 12 fifths obviously cannot produce Ptolemy's "intense diatonic scale", which has been described two lines above as made of 6 fifths, of which one is not perfect (there are other ways to describe it). There would be various ways to extend Prolemy's diatonic scale to 12 degrees but, considering that its tritone already is a syntonic comma wider than the Pythagorean tritone, one might surmise that two such tritones may be lead to an end point two syntonic commas higher than the Pythagorean one – which already is a Pythagorean comma higher than its starting point.

The rest of the Tuning section concerns chromatic scales and equal temperament, and I don't see the reason to include this in an article about diatonic scales. On the other hand, Murray Barbour's Temperament and Tuning describes at least 10 different Greek tunings of the diatonic scale, including Ptolemy's "intense diatonic" under the name of "syntonic diatonic" which indeed makes more sense. A section on the tuning of diatonic scales might probably discuss some of these, instead of digressing to matters that do not concern the diatonic scale.

I would hate to destroy the work of other wikipedians who probably wrote these paragraphs with some specific purpose in mind. This therefore should be considered an appeal to these authors: if there is something that I should have understood better, I would be delighted to know. If not, I may decide to rewrite the section. — Hucbald.SaintAmand (talk) 08:50, 17 April 2018 (UTC)

• @Hucbald.SaintAmand: " I don't see how one may jump twelve fifths" :: this can happen when the music changes key by a fifth upwards, 12 times. Anthony Appleyard (talk) 22:32, 20 April 2018 (UTC)

@Anthony Appleyard: Of course. But even after even only one of these modulations a fifth upwards, the music is no more "in the diatonic scale". The statement "In many diatonic scales, after starting at a note, jumping upwards by a perfect fifth 12 times..." is therefore contradictory. (And why many diatonic scales? It makes no sense.) — Hucbald.SaintAmand (talk) 06:24, 21 April 2018 (UTC)

@Anthony Appleyard: I just saw your editions of Diatonic scale of today. To say that an interval is more "harmonious" if the denominator of the fraction expressing it (after reduction to the highest divider) is lower is wishful thinking. It ressembles what Euler had written on the subject, but only superficially so (Euler did not speak of low figures, but of the factorization of prime numbers), and since Euler the matter has been demonstrated to be quite more complex (e.g. Helmholtz, Stumpf, Terhardt, etc.; see Consonance and dissonance). In addition, the jump from the harmoniousness of intervals to that of chords is unjustifiable.

It is not true that Circle of fifths gives an example of "stepping through the keys from G♭ round the circle to F♯", it merely describes how the circle allows to find the signature for these keys. Musical works stepping through a circle of twelve keys are extremely rare. And they certainly never were meant for the Pythagorean tuning, precisely because the Pythagorean circle does not close on itself. Diatonic scale is misleading on this point – which, in addition, does not concern it.

It is also not true that Ptolemy's intense diatonic scale, if extended to twelve fifth (i.e. to become a chromatic scale), would end with a Pythagorean comma. There would be several ways to extend it (or, better, to extend just intonation, as was frequently done in the 18th century), but none of these extensions could possibly end on a Pythagorean comma, and all of them contain several wolf fifths.

The values given in a table that follows the statement "If x = 12√2 ..." are ridiculous. In this statement, x obviously is the value of the semitone in equal temperament, and it really does not require a table to explain that the tone is equal to two semitones, i.e. to x² – nor that the values of the diatonic scale are 0, 2, 4, 5, 7, 9, 11 and 12 semitones. It does appear "scientific" to say things in this manner, but it is mock science.

I find it unfortunate that such statements in the article turn something that should be simple, the diatonic scale, into something not only unduly complex, but also blatantly false. — Hucbald.SaintAmand (talk) 14:11, 21 April 2018 (UTC)

• @Hucbald.SaintAmand: OK, OK, if it is wrong, then correct it. Sorry. Anthony Appleyard (talk) 15:20, 21 April 2018 (UTC)
• I realize what you are saying. But most people play diatonic-scale music on instruments that can also make all 5 of the usually known sharp and flat notes (= the black keys on a piano), both as needs to change keys and also as accidentals used as special-effects. For example, Wagner once describes a calm forest scene with music which is completely diatonic, except that it has one sharp note to represent a brief wind disturbing the quiet. Anthony Appleyard (talk) 15:36, 21 April 2018 (UTC)
• @Hucbald.SaintAmand: To be more exact, the sung words there included (in German) words like "the wind scarcely disturbed the quiet of the forest", and the German word kaum (= "scarcely") was on a stray accidental sharp note. Anthony Appleyard (talk) 21:20, 21 April 2018 (UTC)
• Similar matter seems to be described in the page Just intonation. Anthony Appleyard (talk) 21:35, 21 April 2018 (UTC)

@Anthony Appleyard: But you do not answer my questions: where does this accidental sharp occur? In what score, and if possible where in that score? Also, how does it occur? Does it result from an additional step in the cycle of fifths (which I doubt), or from a change in the mode of a third (more probable)? If you tell me where, I'll find the answers myself. And does it not in any case mean that the music merely leaves the diatonic scale? I don't think that Just intonation describes anything similar, because the cases quoted there are not from tonal music. But that is another matter anyway.

@Hucbald.SaintAmand: Somewhere in Wagner. I read about it a long time ago. An expert in Wagner should tell you. Call search through Wagner's works (in German) for the word "kaum". Anthony Appleyard (talk) 06:58, 22 April 2018 (UTC)

Your addition to Tuning, in Diatonic scale, "Six of its "fifth" chords (C-G, D-A, E-B; F-C'; G-D'; A-E') are all x7 = about .4983" makes things even worse: (1) these are not chords, but intervals; (2) these are not "six of its fifth chords", they are all of its fifths, the diatonic scale indeed counts only six (and an augmented 4th or a diminished 5th, called the "wolf fifth"); and that they are "x7" (I think "x⁷ would be more understandable) merely means that these fifths are made of 7 semitones (the wolf fifth being made of only 6). And all this should better figure in Equal temperament (it figures there already). — Hucbald.SaintAmand (talk) 06:42, 22 April 2018 (UTC)

@Hucbald.SaintAmand: :: "chords" to "intervals" :: I have changed the word here. Anthony Appleyard (talk) 07:03, 22 April 2018 (UTC)

Tuning of the diatonic scale (part 2)

• @Hucbald.SaintAmand: I am thinking of moving some or most of this new matter to some other page, perhaps Just intonation. (My "x7" for "x⁷" was likeliest an old typo which I had already seen and corrected.) Anthony Appleyard (talk) 10:45, 22 April 2018 (UTC)
• @Hucbald.SaintAmand: See the start of Modulation (music)#Chain modulation for a play link to a piece of music that goes round the circle of fifths in sequential modulation through the circle of fifths in Quartet Op. 3, No. 3, IV, Hob. III:15. Anthony Appleyard (talk) 11:36, 22 April 2018 (UTC)

@Anthony Appleyard: This passage of the quartet op. 3 No 3, which is by Roman Hoffstetter, does not go "round the circle of fifths", despite what the caption might be taken to mean: it only goes through five fifths of the cycle, B−E−A−D−G−C. Such cases are not uncommon, but I repeat that those modulating through the twelve fifths of the circle are extremely rare; they pose a technical problem because in any regular temperament other than equal the circle does not close on itself.

I went through the thirteen operas by Wagner (more than a cycle of fifths, as you can see ;−)) without finding the word kaum in the context that you mention. [I did not actually read these 13 operas, be reassured; I merely visited Richard Wagner Text-Datenbank.] The passage that you mention must come from a Lied, i.e. from a text that is not by Wagner himself. Cases of accidentals outside the local diatonic scale are extremely common, of course. As a matter of fact, this is a point that should probably figure in the article: in common-practice tonal music, keys usually are expressed by being in their own diatonic scale and modulations can be seen as a change of diatonic scale.

Among things that might have to move to other articles, I see the following:

• The names of the degrees, in the section on the Major scale are names of the degrees in the tonal scale; most of them would apply to the minor scale as well (as noted in the following section), but not to the Ionian scale or the other diatonic scales that correspond to the diatonic modes. They are already given in Degree (music), but that article also fails to stress that these names belong to tonal scales.
• It is not always true that "properties [of the diatonic scale] arise from the fact that Western musical theory and notation were conceived with the diatonic scale in mind": it often is the other way around, it is because of these properties that Western music (and its theory and notation) was conceived with the diatonic scale in mind.
• The paragraph concerning David Rothenperg's propriety should easily be replaced by a link to Rothenberg propriety, which itself links to Diatonic set theory, where one reads that "The name is something of a misnomer". I find it a bit strange that an Encyclopedia article must begin by recognizing that its name is a misnomer. At any rate, we should avoid importing the misnomer to Diatonic scale.
• Considerations of consonance should be moved to the article Consonance and dissonance (or should be removed altogether).
• I don't understand the reason for "some" in the sentence "The seven pitches of some diatonic scales can be found from a chain of six perfect fifths." It would be better to start saying that diatonic scales can be tuned variously and add that if they are tuned from a chain of perfect fifths, they will be in Pythagorean tuning.
• If this discussion of the tuning of the diatonic scale is kept here (it could also be moved to Musical tuning and link from there to more specialized articles), I would consider it necessary to discuss the main Greek diatonic tunings (Murray Barbour, pp. 19-21, mentions ten of them. I'd be prepared to write this (sub-)section.
• The paragraph concerning the cycle of 12 fifths and the Pythagorean comma really belongs to Pythagorean tuning, where it probably already can be found, in one way or another.
• I think that the mention of "x = ¹²√2" and what follows should go to Equal temperament.

There are IMO major problems in most of the articles quoted above. See also my comments in Talk:Meantone_temperament. But if we could solve those of Diatonic scale, it would be a good first step. — Hucbald.SaintAmand (talk) 13:38, 22 April 2018 (UTC)

Tuning chart of Fifths

I don't get the same results as the chart. My math says to go from E to F, is to multiply by 256/243, making that an imperfect interval. From A to B I get a perfect 9/8 interval. I am really confused, can't do math, or the chart is incorrect. I will let smarter people fix this, in case I am confused.

2601:281:CB00:2A0:6CAB:B482:7826:FF12 (talk) 01:11, 27 February 2019 (UTC)

The chart is indeed misleading in that it describes "pitches" in terms of ratios and that it gives the ratios under the degrees (instead of between them). What is meant in the lines marked "pitch" is the interval from the initial note (C), i.e. the cumulation of the intervals between notes.

You are perfectly right and the semitone E–F should be the same as B–C, 256/243, the Pythagorean limma (i.e. diatonic semitone). On the other hand, A–B is correctly identified in the chart as 9/8.

The presentation of the chart could be improved. I'll change the captions and the figures without waiting. If anyone is familiar with the construction of WP charts, she/he might arrange that the ratios appear between the degrees. Otherwise I'll try to get information on how to do that, and I'll change it myself. — Hucbald.SaintAmand (talk) 08:55, 27 February 2019 (UTC)

January 2022

What is the correct pattern of diatonic scale?

• A. WS-WS-HS-WS-WS-WS-HS
• B. WS-WS-HS-HS-WS-WS-HS
• C. WS-WS-WH-WH-WS-WS-WH
• D. WS-WH-WS-WH-WS-WH-WS

— Preceding unsigned comment added by 119.93.219.248 (talk) 02:38, 1 January 2022 (UTC)

Could you explain what you mean by "WS", "HS" and "WH"? Supposing that WS is a tone (2 semitones) and HS is a semitone, your list becomes:

• A. 2–2–1–2–2–2–1 = 12 semitones
• B. 2–2–1–1–2–2–1 = 11 semitones
• C. 2–2–?–?–2–2–? = ? semitones
• D. 2–?–2–?–2–?–2 = ? semitones

As you see, I don't know what WS means, so that I cannot compute the number of semitones.

Scale A. is one diatonic scale among several. The main definition of a diatonic scale is that it has five tones and two semitones, the latter being maximally distant (i.e. distant by either two or three tones); there are seven ways to built such scales, which could also be defined as rotations of your scale A. The total in each case is 12 semitones.

Scale B. is not diatonic (if my translations of WS and HS are correct) because it includes three semitones, of which two following each other. Also, with only 11 semitones, it does not reach the octave. (Reaching the octave might be the definition of a scale, in this context at least.)

Again, I don't figure what WH means; it might be 1½ semitone (or any other interval), but a diatonic scale should include only two types of intervals, tones and semitones.

Hucbald.SaintAmand (talk) 09:59, 1 January 2022 (UTC)

Music

How to use a musical scale on Bass 41.190.2.209 (talk) 08:42, 3 May 2022 (UTC)

White notes?

In the third paragraph, the phrase “the white notes” bothers me. I would think a better phrasing would be “the notes on the white keys,” but I don’t feel confident enough to make the change myself. MozzieM (talk) 11:42, 4 January 2023 (UTC)

I changed this into "white-key notes", in the hope that it makes better sense. Some might argue that the white keys ain't always white, but I leave it to them to do better. — Hucbald.SaintAmand (talk) 14:13, 4 January 2023 (UTC)

First known use of the word "diatonic"

Webster's says the first known use of the word "diatonic" is in 1694. https://www.merriam-webster.com/dictionary/diatonic I was curious to know that first use. Then I come to this article and its history is way older than 1694. Anybody know that first use Websters refers to? If Webster's thinks that's the first use, what was it called before? WithGLEE (talk) 14:05, 31 December 2023 (UTC)

Webster must be thinking of the English term. The date 1694 might refer to John Playford, Breefe Introduction to the Skill of Musick, but this is the 12th edition of a treatise that is much older (1654), and I don't find the word in the 12th edition. Or it may refer to William Holder, A treatise on the natural grounds and principles of harmony, of which I have only a later edition (1731), which does use the word.

The Online Etimology Dictionary gives an earlier date for diatonic, c.1600, but gives no precise reference, and I can't think of a music treatise in English by that time. Etymonline merely adds "in ancient Greek music" and gives the same origin as Webster does, in French, Latin, and Greek. It goes without saying that if words in Greek, Latin or French were to be considered, the date would be much earlier, back to Pythagoras' time in the 6th century BC and perhaps earlier. — Hucbald.SaintAmand (talk) 15:45, 31 December 2023 (UTC)

A few queries

Hi, I've just made minor adjustments to the opening, without changing the substantive meaning. And I've extended the caption for the first example to actually state which intervals are the semitones—rather pointless without that. "depending on their position in the scale" seemed redundant, so I deleted it to solve the problem of which intervals "their" refers to: whole tones or semitones? It's not obvious.

The second paragraph: I wonder why this chain of six perfect fifths is introduced so early. It's not necessary to understand what a diatonic scale is; and it's much less relevant to the diatonic "church modes", which began without the primacy of the fifth.

I also wonder why set theory is introduced so early, too: it's bound to turn off the non-expert reader. And could we have a reference for it please? Tony (talk) 11:44, 8 November 2024 (UTC)

The article also writes:

A diatonic scale can be also described as two tetrachords separated by a whole tone.

But that obviously is wrong. B C D E and F G A B are (or can be considered) tetrachords separated by a semitone. Or, if one considers that they are not tetrachords because they don't span a perfect fourth, the diatonic scale is not always formed of tetrachrods. I am not convinced by the affirmation of the tetrachords article that tetrachords "in traditional music theory" (???) must span a perfect fourth. In addition, it seems to me that the description of the diatonic scale as formed of two tetrachords is old fashioned, based on late 19th and early 20th century misconceptions of antique Greek theory. — Hucbald.SaintAmand (talk) 12:56, 8 November 2024 (UTC)

Agreed. Tony (talk) 01:59, 9 November 2024 (UTC)